does a model differ from a theory

Problem 61GP Starting from its nest, an eagle flies at constant speed for 3.0 min due east, then 4.0 min due north. From there the eagle flies directly to its nest at the same speed. How long is the eagle in the air?

Problem 60GP A large passenger aircraft accelerates down the runway for a distance of 3000 m before leaving the ground. It then climbs at a steady 3.0° angle. After the plane has traveled 3000 m along this new trajectory, (a) how high is it, and (b) how far horizontally is it, from its initial position?

Problem 59GP The sun is 30° above the horizon. It makes a 52-m-long shadow of a tall tree. How high is the tree?

Problem 58GP In 2003, the population of the United States was 291 million people. The per-capita income was $31,459. What was the total income of everyone in the United States? Express your answer in scientific notation, with the correct number of significant figures.

Problem 57GP The bacterium Escherichia coli (or E. coli) is a single celled organism that lives in the gut of healthy humans and animals. When grown in a uniform medium rich in salts and amino acids, it swims along zigzag paths at a constant speed changing direction at varying time intervals. Figure P1.61 shows the positions of an E. coli as it moves from point A to point J. Each segment of the motion can be identified by two letters, such as segment BC. During which segments, if any, does the bacterium have the same a. Displacement? b. Speed? c. Velocity?

Why is it incorrect to think that the more digits you include in your answer, the more accurate it is?

The diameter of the Moon is 3480 km. What is the volume of the Moon? How may Moons would be needed to create a volume equal to that of Earth?

Problem 50GP A watch manufacturer claims that its watches gain or lose no more than 8 seconds in a year. How accurate are these watches, expressed as a percentage?

Problem 56GP The bacterium Escherichia coli (or E. coli) is a single celled organism that lives in the gut of healthy humans and animals. Its body shape can be modeled as a 2-?m-long cylinder with a 1 ?m diameter, and it has a mass of . Its chromosome consists of a single double-stranded chain of DNA 700 times longer than its body length. The bacterium moves at a constant speed of 20 ?m/s, though not always in the same direction. Answer the following questions about E. coli using SI units (unless specifically requested otherwise) and correct significant figures. a. What is its length? b. Diameter? c. Mass? d. What is the length of its DNA, in millimeters? e. If the organism were to move along a straight path, how many meters would it travel in one day?

Problem 52GP An angstrom (symbol A) Is a unit of length, defined as 10-10 which is on the order of the diameter of an atom, (a) How many nanometers are in 1.0 angstrom? (b) How many femtometers or fermis (the common unit of length in nuclear physics) are in 1.0 angstrom? (c) How many angstroms are in 1.0 m? (d) How many angstroms are in 1.0 light-year (see Problem 19)?

Problem 53GP Determine the percent uncertainty in ? and in sin ?, when (a) ? = 15° ± 0.5°, (b) ? =75 0° ± 0.5°.

If you began walking along one of Earth's lines of longitude and walked until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is called a "nautical mile."

Problem 55GP Your brain communicates with your body using ?nerve imp? ulses, electrical signals propagated along axons. Axons come in two varieties: insulated axons with a sheath made of myelin, and uninsulated axons with no such sheath. Myelinated (sheathed) axons conduct nerve impulses much faster than unmyelinated (unsheathed) axons. The impulse speed depends on the diameter of the axons and the sheath, but a typical myelinated axon transmits nerve impulses at a speed of about 25 m/s, much faster than the typical 2.0 m/s for an unmyelinated axon. Figure 55 shows three equal-length nerve fibers consisting of eight axons in a row. Nerve impulses enter at the left side simultaneously and travel to the right. a. Draw motion diagrams for the nerve impulses traveling along fibers A, B, and C. b. Which nerve impulse arrives at the right side first? c. Which will be last? FIGURE 55

Problem 1PE Problem The speed limit on some interstate highways is roughly 100 km/h. (a) What is this in meters per second? (b) How many miles per hour is this?

Problem 2CQ Problem How does a model differ from a theory?

Problem 2P (I) How many significant figures do each of the following numbers have: (a) 214, (b) 81.60, (c) 7.03, (d) 0.03, (e) 0.0086. (f) 3236. and (g) 8700?

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in (a) years, (b) seconds.

Problem 1CQ a. Write a paragraph describing the particle model. What is it, and why is it important? b. Give two examples of situations, different from those described in the text, for which the particle model is appropriate. c. Give an example of a situation, different from those described in the text, for which it would be inappropriate.

Problem 2PE A car is traveling at a speed of 33 m/s . (a) What is its speed in kilometers per hour? (b) Is it exceeding the 90 km/h speed limit?

Problem 3CQ If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both use accepted rules of logic)?

Problem 3PE Show that 1.0 m/s = 3.6 km/h . Hint: Show the explicit steps involved in converting 1.0 m/s = 3.6 km/h.

(Note: In Problems, assume a number like 6.4 is accurate to \(\pm 0.1\) ; and 950 is \(\pm 10\) unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 \(\pm 1\).) Write the following numbers in powers of ten notation: (a) 1.156, (b) 21.8, (c) 0.0068, (d) 27.635, (e) 0.219 and (f) 444.

A ball is dropped from the roof of a tall building and students in a physics class are asked to sketch a motion diagram for this situation. A student submits the diagram shown in Figure Q1.4. Is the diagram correct? Explain.

Problem 4PE American football is played on a 100-yd-long field, excluding the end zones. How long is the field in meters? (Assume that 1 meter equals 3.281 feet.)

What is wrong with this road sign: Memphis 7 mi (11.263 km)?

Problem 5CQ Write a sentence or two describing the difference between position and displacement. Give one example of each.

Problem 5PE Soccer fields vary in size. A large soccer field is 115 m long and 85 m wide. What are its dimensions in feet and inches? (Assume that 1 meter equals 3.281 feet.)

Problem 5P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) (II) What, approximately, is the percent uncertainty for a measurement given as 1.57 m2?

For an answer to be complete, the units need to be specified. Why?

Problem 6CQ Give an example of a trip you might take in your car for which the distance traveled as measured on your car’s odometer is not equal to the displacement between your initial and final positions.

Problem 7CQ Classical physics is a good approximation to modern physics under certain circumstances. What are they?

What is the height in meters of a person who is 6 ft 1.0 in. tall? (Assume that 1 meter equals 39.37 in.)

Problem 6P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) What is the percent uncertainty in the measurement 3.76 0,25 m?

Problem 7P A new generation of pogo sticks lets a rider bounce more than 2 meters off the ground by using elastic bands to store energy. When the pogo’s plunger hits the ground, the elastic bands stretch as the pogo and rider come to rest. At the low point of the bounce, the stretched bands start to contract, pushing out the plunger and launching the rider into the air. For a total mass of 80kg (rider plus pogo), a stretch of 0.40 m launches a rider 2.0 m above the starting point. Suppose a much smaller rider (total mass of rider plus pogo of 40 kg) mechanically stretched the elastic bands of the pogo by 0.40 m, then got on the pogo and released the bands. How high would this unwise rider go? A. 8.0 m B. 6.0 m C. 4.0 m D. 3.0 m

Problem 7P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent certainty of a hand timed measurements of (a) 5 s, (b) 50 s (c) 5 min?

Problem 7Q You measure the radius of a wheel to be 4.16 cm. If you multiply by 2 to get the diameter, should you write the result as 8 cm or as 8.32 cm? Justify your answer.

Express the sine of 30.0° with the correct number of significant figures.

Problem 8P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) Add (9.2 x 103s) + (8.3 x 104s)

Problem 9P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) Multiply 2.079 x 102 m by 0.082 x 10-1, taking into account significant figures.

Problem 10P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) What is the area, and its approximate uncertainty, of a circle of radius 3.8 x 104 cm?

Problem 10Q List assumptions useful to estimate the number of car mechanics in (a) San Francisco, (b) your hometown, and then make the estimates.

Problem 11P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 0.09 m?

Problem 12P Write the following as full (decimal) Numbers with standard units: (a) 286.6 mm, (b) 85 V, (c) 760 mg, (d) 60.0 ps, (e) 22.5 fm, (f) 2.50 gigavolts

(I) Express the following using the prefixes of Table : (a) \(1 \times 10^{6}\) volts, (b) \(2 \times 10^{-6}\) meters. (c) \(6 \times 10^{3}\) days, (d) \(18 \times 10^{2}\) bucks, and (e) \(8 \times 10^{-9}\) pieces. Equation Transcription: Text Transcription: 1 x 106 2 x 10-6 6 x 103 18 x 102 8 x 10-9

Problem 14P Determine your own height in meters, and your mass in kg.

Problem 11P (Note: In Problems, assume a number like 6.4 is accurate to ; and 950 is unless 950 is said to be “precisely” or “very nearly 950, in which case assume 950 ) What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 0.09 m?

Problem 17P An aiplane travels at 950 km/h. How long does it take to travel 1.00 km?

Problem 18P (II) A typical atom has a diameter of about 1.0 X 10-10 (a) What is this in inches? (b) Approximately how many atoms are along a 1.0-cm line, assuming they just touch?

(II) Express the following sum with the correct number of significant figures: \(1.80\text{m}+142.5\text{cm}+5.34\times 10^5\mu \text{m}\)

Problem 20P (II) Determine the conversion factor between (a) km/h and mi/h and ft/s and (c) km/h and m/s.

Problem 21AIP Football players measure their acceleration by seeing how fast they can sprint 40 yards (37 m). A zippy player can, from a standing start, run 40 yards in 4.1 s, reaching a top speed of about 11 m/s. For an 80kg player, what is the average power output for this sprint? A. 300 W B. 600 W C. 900 W D. 1200 W

Problem 21P (II) How much longer (percentage) is a one-mile race than a 1500-m race ("the metric mile”)?

Problem 22P (II) A light-year is the distance light travels in one year (at speed = 2.998 X 108 m/s)(a) How many meters are there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth. 1.50 X 108 km How many AU are there in 1.00 light-year?

Problem 23AIP A 100 kg football player is moving at 6.0 m/s to the east; a 130 kg player is moving at 5.0 m/s to the west. They meet, each jumping into the air and grabbing the other player. While they are still in the air, which way is the pair moving, and how fast?

Problem 24AIP A swift blow with the hand can break a pine board. As the hand hits the board, the kinetic energy of the hand is transformed into elastic potential energy of the bending board; if the board bends far enough, it breaks. Applying a force to the center of a particular pine board deflects the center of the board by a distance that increases in proportion to the force. Ultimately the board breaks at an applied force of 800 N and a deflection of 1.2 cm. a. To break the board with a blow from the hand, how fast must the hand be moving? Use 0.50 kg for the mass of the hand. b. If the hand is moving this fast and comes to rest in a distance of 1.2 cm, what is the average force on the hand?

Problem 24PE Express your answers to problems in this section to the correct number of significant figures and proper units. A marathon runner completes a 42.188-km course in 2 h , 30 min, and 12 s . There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the uncertainty in the elapsed time. (c) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?

Problem 25PE Express your answers to problems in this section to the correct number of significant figures and proper units. The sides of a small rectangular box are measured to be 1.80 ± 0.01 cm , 2.05 ± 0.02 cm, and 3.1 ± 0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

Problem 26PE Express your answers to problems in this section to the correct number of significant figures and proper units. When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass (lbm) was employed, where 1 lbm = 0.4539 kg . (a) If there is an uncertainty of 0.0001 kg in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of 1 kg when converted to kilograms?

Problem 25AIP A child’s sled has rails that slide with little friction across the snow. Logan has an old wooden sled with heavy iron rails that has a mass of 10 kg—quite a bit for a 30 kg child! Logan runs at 4.0 m/s and leaps onto the stationary sled and holds on tight as it slides forward. The impact time with the sled is 0.25 s. a. Immediately after Logan jumps on the sled, how fast is it moving? b. What was the force on the sled during the impact? c. How much energy was “lost” in the impact? Where did this energy go?

Problem 27PE Express your answers to problems in this section to the correct number of significant figures and proper units. The length and width of a rectangular room are measured to be 3.955 ± 0.005 m and 3.050 ± 0.005 m . Calculate the area of the room and its uncertainty in square meters.

Problem 28PE Express your answers to problems in this section to the correct number of significant figures and proper units. A car engine moves a piston with a circular cross section of 7.500 ± 0.002 cm diameter a distance of 3.250 ± 0.001 cm to compress the gas in the cylinder. (a) By what amount is the gas decreased in volume in cubic centimeters? (b) Find the uncertainty in this volume.

Problem 29PE How many heartbeats are there in a lifetime?

Problem 30PE A generation is about one-third of a lifetime. Approximately how many generations have passed since the year 0 AD?

Problem 31PE How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of 10?22 s .)

Problem 32PE Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of 10?27 kg and the mass of a bacterium is on the order of 10?15 kg.) Figure 1.28 This color-enhanced photo shows Salmonella typhimurium (red) attacking human cells. These bacteria are commonly known for causing foodborne illness. Can you estimate the number of atoms in each bacterium? (credit: Rocky Mountain Laboratories, NIAID, NIH)

Problem 33PE Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?

Problem 34PE (a) What fraction of Earth’s diameter is the greatest ocean depth? (b) The greatest mountain height?

Problem 35PE (a) Calculate the number of cells in a hummingbird assuming the mass of an average cell is ten times the mass of a bacterium. (b) Making the same assumption, how many cells are there in a human?

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?

Problem 8PE The speed of sound is measured to be 342 m/s on a certain day. What is this in km/h?

Problem 9PE Tectonic plates are large segments of the Earth’s crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

Problem 8CQ When is it necessary to use relativistic quantum mechanics?

Problem 4P (Note: In Problems, assume a number like 6.4 is accurate to ?0.1: and 950 is ? 10 unless 950 is said to be ?precisely? or ?very nearly? 950. in which case assume 950 ? 1.) (I) Write out the following numbers in full with the correct number of zeros: (a) 8.69 X 104 (b) 9.1 X 103, (c) 8.8 X 10-1 (d) 4.76 X 102 and (e) 3.62 X 10-5.

Problem 9CQ Can classical physics be used to accurately describe a satellite moving at a speed of 7500 m/s? Explain why or why not.

Problem 10CQ Identify some advantages of metric units.

Problem 11CQ What is the relationship between the accuracy and uncertainty of a measurement?

Problem 11PE Express your answers to problems in this section to the correct number of significant figures and proper units. Suppose that your bathroom scale reads your mass as 65 kg with a 3% uncertainty. What is the uncertainty in your mass (in kilograms)?

Problem 12CQ Prescriptions for vision correction are given in units called diopters (D). Determine the meaning of that unit. Obtain information (perhaps by calling an optometrist or performing an internet search) on the minimum uncertainty with which corrections in diopters are determined and the accuracy with which corrective lenses can be produced. Discuss the sources of uncertainties in both the prescription and accuracy in the manufacture of lenses.

Problem 12PE Express your answers to problems in this section to the correct number significant figures and proper units. A good-quality measuring tape can be off by 0.50 cm over a distance of 20 m. What is its percent uncertainty?

Problem 13PE Express your answers to problems in this section to the correct number of significant figures and proper units. (a) A car speedometer has a 5.0% uncertainty. What is the range of possible speeds when it reads 90 km/h ? (b) Convert this range to miles per hour. (1 km = 0.6214 mi)

Problem 14PE Express your answers to problems in this section to the correct number of significant figures and proper units. An infant’s pulse rate is measured to be 130 ± 5 beats/ min. What is the percent uncertainty in this measurement?

Problem 16PE Express your answers to problems in this section to the correct number of significant figures and proper units. A can contains 375 mL of soda. How much is left after 308 mL is removed?

Problem 17PE Express your answers to problems in this section to the correct number of significant figures and proper units. State how many significant figures are proper in the results of the following calculations: (a)(106.7)(98.2) / (46.210)(1.01) (b) (18.7)2 (c) (1.60×10?19)(3712) .

Problem 15PE Express your answers to problems in this section to the correct number of significant figures and proper units. a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y? (b) In 2.00 y? (c) In 2.000 y?

Problem 18PE Express your answers to problems in this section to the correct number of significant figures and proper units. (a) How many significant figures are in the numbers 99 and 100? (b) If the uncertainty in each number is 1, what is the percent uncertainty in each? (c) Which is a more meaningful way to express the accuracy of these two numbers, significant figures or percent uncertaintie

Problem 19PE Express your answers to problems in this section to the correct number of significant figures and proper units. (a) If your speedometer has an uncertainty of 2.0 km/h at a speed of 90 km/h , what is the percent uncertainty? (b) If it has the same percent uncertainty when it reads 60 km/h , what is the range of speeds you could be going?

Problem 20PE Express your answers to problems in this section to the correct number of significant figures and proper units. (a) A person’s blood pressure is measured to be 120 ± 2 mm Hg . What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg ?

Problem 21P Express your answers to problems in this section to the correct number of significant figures and proper units. A person measures his or her heart rate by counting the number of beats in 30 s. If 40 ± 1 beats are counted in 30.0 ± 0.5 s , what is the heart rate and its uncertainty in beats per minute?

Problem 22PE Express your answers to problems in this section to the correct number of significant figures and proper units. What is the area of a circle 3.102 cm in diameter?

Problem 23PE Express your answers to problems in this section to the correct number of significant figures and proper units. If a marathon runner averages 9.5 mi/h, how long does it take him or her to run a 26.22-mi marathon?

Problem 3RE Equations of lines Find an equation of the lines with the following properties. Graph the lines. a. The line passing through the points (2, ?3) and (4, 2) b. The line with slope ? and x? -intercept (?4, 0) c. The line with intercepts (4, 0) and (0, ?2)

Problem 2RE Domain and range Find the domain and range of the following functions. ? ? a.??f? ) ? x5+ ? ? b. ?g(? )= ? ? c. ?h(? )=

Problem 5RE Graphing absolute value: Consider the function ? ? f(?? ) = 2? (?x ? | ?x |). Express the function in two pieces without using the absolute value. Then graph the function by hand. Use a graphing utility only to check your work.

Problem 4RE Piece wise linear functions: The parking costs in a city garage are $2.00 for the first half hour and $ 1.00 for each additional half hour. Graph the fun?ctio ? n? = ?f(?t) that gives the cost of park?ing for ? hours, wh?ere 0 ? t? ? 3.

Problem 1RE Explain why or why not. Determine whether the following statements are true and give an explanation or counter example. a. A function could have the property that ?f?(x ? ?) =? ?(? ? for all ? . b. cos (a? ? +? ?)= cos ?a? + cos ?b? for all? ? and ?b? in [0, 2?? . c. If ?f? is a linear function of the form ?f?(?x?) = ?mx? + ?b?,then ?f?(?u? + ?v?)= ?f?(?u?)+ ?f?(?v?)for all ?u and v? . d. The function f ? ?(? ? 1 ? ? ? has the property ?f(f(x)) = x e. The set {?x?: | ?x? + 3| > 4} can be drawn on the number line without lifting your pencil. f. logic (x? y?) = (logl0 ? ? (logl0 ?y?). g. sin?1 (sin ?(2??))= 0.

Problem 6RE Function from words: Suppose you plan to take a 500-mi trip in a car that gets 35 mi/gal. Find the fun?ctio ? n? = ?f(?p)that gives the cost of gasoline for the trip when gasoline costs ? $p per gallon.

Problem 7RE Graphing equations: Graph the following equations. Use a graphing utility only to check your work. ? a?. 2?x ? 3y ? + 10 = 0 ? ? b.??y = ?x2+ 2?x ? 3 ? ? c? . ?x2 +? 2x? + y ? 2 + 4y ? + 1 = 0 ? ? ? d? .? 7??? 2x ? + y?2 ? 8?y + 5 = 0

Problem 1Q: What are the merits and drawbacks of using a person’s foot as a standard? Consider both (a) a particular person’s foot, and (b) any person’s foot. Keep in mind that it is advantageous that fundamental standards be accessible (easy to compare to), Invariable (do not change), indestructible and reproducible.

Problem 2Q When traveling a highway in the mountains, you may see elevation signs that read “914m (3000 ft).” Critics of the metric system claim that such numbers show the metric system is more complicated. How would you alter such signs to be more consistent with a switch to the metric system

Problem 6Q Discuss how the notion of symmetry could be used to estimate the number of marbles in a 1-liter jar.

A recipe for a soufflé specifies that the measured ingredients must be exact, or the soufflé will not rise. The recipe calls for 6 large eggs. The size of "large" eggs can vary by 10%, according to the USDA specifications. What does this tell you about how exactly you need to measure the other ingredients?

Problem 16P What is the conversion factor between (a) ft2 and yd2, (b) m2 and ft2?

(II) Estimate how many books can be shelved in a college library with 3500 square meters of floor space. Assume 8 shelves high, having books on both sides, with corridors \(1.5 \mathrm{~m}\) wide. Assume books are about the size of this one, on average.

(II) Estimate how many hours it would take to run (at 10 km/h ) across the U S. from New York to California.

(II) Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 1-13). Assume the mower moves with a 1 km/h speed, and has a 0.5 m width.

(II) Estimate the number of liters of water a human drinks in a lifetime.

Problem 23P The diameter of the moon is 3480 km. (a) what is the surface area of the Moon? (b) How many times larger is the surface area of the Earth?

(Note: Remember that for rough estimates, only round numbers are needed both as input to calculations and as final results.) (I) Estimate the order of magnitude (power of ten) of: (a) 2800, (b) \(86.30 \times 10^{2}\) (c) 0.0076, and (d) \(15.0 \times 10^{8}\).

(II) Three students derive the following equations in which x refers to distance traveled, v the speed, a the acceleration \(\left(\mathrm{m} / \mathrm{s}^2\right)\), and t the time, and the subscript (0) means a quantity at time \(t=0:(a) x=v t^2+2 a t\), (b) \(x=v_0 t+\frac{1}{2} a t^2\), and (c) \(x=v_0 t+2 a t^2\). Which of these could possibly be correct according to a dimensional check?

Problem 29P (Note: Remember that for rough estimates, only round numbers are needed both as input to calculations and as final results.) Make a rough estimate of the volume of your body (in cm3).

Problem 30P (Note: Remember that for rough estimates, only round numbers are needed both as input to calculations and as final results.) Make a rough estimate, for a typical suburban house, of the % of its outside wall area that consists of window area.

(III) The rubber worn from tires mostly enters the atmosphere as particulate pollution. Estimate how much rubber (in \(\mathrm{kg}\) ) is put into the air in the United States every year. To get started, a good estimate for a tire tread's depth is \(1 \mathrm{~cm}\) when new, and the density of rubber is about \(1200 \mathrm{~kg} / \mathrm{m}^3\).

Problem 32P The Speed, v, of an object is given by the equation v=At3 - Bt, where t refers to ime. WHat re the dimensions of A and B?

Problem 34GP Global positioning satellites (GPS) can be used to determine position with great accuracy. The system works by determining the distance between the observer and each of several satellites orbiting Earth. If one of the satellites is at a distance of 20,000 km from you, what percent accuracy in the distance is required if we desire a 2-meter uncertainty? How many significant figures do we need to have in the distance?

Computer chips (Fig. 1-14) are etched on circular silicon wafers of thickness \(0.60 \mathrm{~mm}\) that are sliced from a solid cylindrical silicon crystal of length \(30 \mathrm{~cm}\). If each wafer can hold 100 chips, what is the maximum number of chips that can be produced from one entire cylinder? FIGURE 1-14 Problem 35. The wafer held by the hand (above) is shown below, enlarged and illuminated by colored light. Visible are rows of integrated circuits (chips).

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. 1-16). Make appropriate measurements to estimate the diameter of the Moon, given that the Earth-Moon distance is \(3.8 \times 10^{5} \mathrm{~km}\) Equation Transcription: Text Transcription: 3.8 X 10^5 km

(a) How many seconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?

A typical adult human lung contains about 300 million tiny cavities called alveoli. Estimate the average diameter of a single alveolus.

One liter \(\left(1000 \mathrm{~cm}^3\right)\) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of \(2 \times 10^{-10} \mathrm{~m}\).

Problem 38GP One hectare is defined as 104 m2. One acre is 4 x 104 ft2. How many acres are in one hectare?

Use Table 1-3 to estimate the total number of protons or neutrons in (a) a bacterium, (b) a DNA molecule, (c) the human body, (d) our Galaxy.

Estimate the number of gallons of gasoline consumed by the total of all automobile drivers in the United States, per year.

Estimate the number of gumballs in the machine of Fig. 1 - 15

Problem 42GP An average family of four uses roughly 1200 liters (about 300 gallons) of water per day. (one liter = 1000 cm3.) How much depth would a lake lose per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of 40,000 people? Consider only population uses, and neglect evaporation and so on.

Problem 43GP How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1 kg per liter (103cm3) or 62 lb per cubic foot.]

Problem 44GP A heavy rainstorm dumps 1.0 cm of rain on a city 5 km wide and 8 k long in a 2-h period. How many metric tons (1 metric ton = 103 kg) of water fell on the city? [ 1 cm3 of water has a mass of 1 gram = 10-3kg.] How many gallons of water was this?

Estimate how many days it would take to walk around the world, assuming \(10 \mathrm{~h}\) walking per day at \(4 \mathrm{~km} / \mathrm{h}\).

Problem 47GP Noah’s ark was ordered to be 300 cubits long, 50 cubits wide, and 30 cubits high. Tire cubit was a unit of measure equal to the length of a human forearm, elbow to the top of the longest finger. Express the dimension of Noah’s ark in meters, and estimate its volume (m3).

Jean camps beside a wide river and wonders how wide it is. She spots a large rock on the bank directly across from her. She then walks upstream until she judges that the angle between her and the rock, which she can still see clearly, is now at an angle of \(30^{\circ}\) downstream (Fig, 1-17). Jean measures her stride to be about one yard long. The distance back to her camp is 120 strides. About how far across, both in yards and in meters, is the river? Equation Transcription: Text Transcription: 30^\circ